Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class A
{
    BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = null;
    
    private void solve() throws IOException
    {
        int n = 2 * nextInt();
        for(int i = 1; i * i <= n; i++)
        {
            if(bs(i * (i + 1), n))
            {
                System.out.println("YES");
                return;
            }
            
        }
        
        System.out.println("NO");
    }
    
    private boolean bs(int k, int n)
    {
        int l = 1;
        int r = (int) Math.sqrt(n);
        while(l <= r)
        {
            int m = (l + r) / 2;
            int ss = m * (m + 1) + k;
            if(ss == n)
            {
                return true;
            }
            else if(ss > n)
            {
                r = m - 1;
            }
            else
            {
                l = m + 1;
            }
            
        }
        
        return false;
    }
    
    String nextToken() throws IOException
    {
        if (st == null || !st.hasMoreTokens())
        {
            st = new StringTokenizer(bf.readLine());
        }
        
        return st.nextToken();
    }

    int nextInt() throws IOException
    {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException
    {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException
    {
        return Double.parseDouble(nextToken());
    }

    public static void main(String args[]) throws IOException
    {
        new A().solve();
    }
    
}